Horses would often be swapped out at stations when a wealthy person would have to travel very quickly across a long distance. Maybe this is an average since the speed with which horsemen could travel would depend on the rate at which they exchanged their horses.
In an extreme example from the year 9 BC, the future emperor Tiberius traveled on the Roman Roads 330 miles (531 km) between northern Italy and modern day Mainz, Germany in 36 hours without sleep. He was rushing to the deathbed of his older brother Drusus after the latter suffered mortal injuries in a freak horse accident. https://en.wikipedia.org/wiki/Drususstein
In an extreme example from the year 9 BC, the future emperor Tiberius traveled on the Roman Roads 330 miles (531 km) between northern Italy and modern day Mainz, Germany in 36 hours without sleep. He was rushing to the deathbed of his older brother Drusus after the latter suffered mortal injuries in a freak horse accident. https://en.wikipedia.org/wiki/Drususstein